Electron localization in disordered quantum systems at finite temperatures

Abstract

We study electron localization in disordered quantum systems, focusing on both individual eigenstates and thermal states. We employ complex polarization as a numerical indicator to characterize the system's localization length. Furthermore, we assess the efficacy of mean-field approximation in providing a quantitative analysis of such systems. Through this study, we seek to provide insight into the following aspects: the behavior of electron localization as a function of interaction, disorder, and temperature, whether thermal states and highly excited states exhibit similar properties in many-body localized systems, and the reliability of the mean-field approximation in weak-interaction scenarios.